I do not know that the Prophet of Allah ﷺ ever recited the entire Quran in a single night until morning.
حدثنا أبو بكر بن أبي شيبة حدثنا محمد بن بشر حدثنا سعيد بن أبي عروبة حدثنا قتادة عن زرارة بن أوفى عن سعد بن هشام
لا أعلم نبي الله ﷺ قرأ القرآن كله حتى الصباح
Sourcing, [sahih] Nasai narrated it, 3/218, Qiyam al-Layl, "The Disagreement Regarding Ayesha's Account of Reviving the Night in Prayer," hadith 1642, and others narrated it from the hadith of Saeed with this wording, and its wording is, "I do not know of the Messenger of Allah ﷺ ever reciting the whole Quran in one night, nor standing in prayer through an entire night until morning, nor fasting a complete month other than Ramadan."Saeed stated explicitly that he heard it directly (Nasai, hadith 2350). Qatada narrated with an ambiguous form (an), but his hadith has many corroborating witnesses.